I haven't used surface modeling tools that much so I'm bit lost at the moment how to model this correctly.

As seen below a debossed Wrap around a imaginary cylinder produces solution which is ~close but I can't figure out how to make the rotating surface perpendicular to conical face... (Also tried this​ but can't get my head over how I should transform my sketch to get that to work...)

Sketch:

Wrap (deboss):

What I'm looking for: